Please help us continue having these discussions by supporting us over on Patreon: https://www.patreon.com/c/SolomonSmith

Kirwin's article on mathematics is available here: https://kirwinhampshire.substack.com/p/the-dark-night-of-mathematics

In this episode of Solomon and Smith, Jack and Milo speak with Kirwin Hampshire, mathematics PhD and author of the Substack Ossuray Lost at Sea.

Is mathematics discovered or invented? Is it a formal game, a spiritual art form, a machine for generating truth, or the highest expression of human creativity? And what happens when AI begins solving open problems, producing counterexamples, and doing the thing mathematicians thought belonged to the strange, private, intuitive life of the mind?

We discuss what a number is, why mathematics feels certain in a way other forms of knowledge often do not, whether infinity and zero expand the limits of thought, and why mathematical discovery can feel closer to art, wizardry, or religious revelation than to ordinary technical work. Then we turn to the nightmare: AI-generated mathematics, the psychology of being scooped by a machine, and the possibility that human mathematicians may be reduced to checking, verifying, and understanding what machines have already produced.

Is AI killing maths? Or is it revealing what mathematics really was all along?

Topics include: AI and mathematics, mathematical creativity, open problems, counterexamples, proof, intuition, infinity, zero, Gödel, Cantor, mathematical beauty, the philosophy of maths, AI art, chess engines, human purpose, dangerous knowledge, truth versus goodness, and whether machines are about to ruin the most beautiful thing humans ever made.

Chapters:

00:00 AI and the human gap

01:15 Introduction

05:58 The challenge

07:37 Kirwin enters

10:00 Poetic epigraph

11:37 What is a number?

17:11 Maths, mind, and reality

20:37 Mathematics as creativity

22:30 Infinity and the machinery of thought

26:45 Falling in love with maths

32:15 Discovery, invention and the unfinished painting

37:14 Has maths become too arcane?

41:35 AI enters mathematics

44:11 AI counterexamples and open problems

49:39 Chess, machines and the loss of spark

52:36 Humans as the AI’s assistant

57:22 Intuition and the human gap

1:02:34 Dangerous truth and the Copernican trauma

1:06:50 The Impossible Luddite

1:13:40 Why does AI hurt?

1:16:12 Is AI just another tool?

1:21:17 Truth, beauty and incompatible desires

1:24:08 Process versus result

Performance of the second movement from Bartók's second quartet by the Carmel Quartet, used under the following license: https://creativecommons.org/licenses/by/3.0/deed.en